Depth of field is an important concept in photography, here is what it is.
As you may know, every real point in front of the lens creates an image on the film/sensor. Only when the image of a point is smaller than the resolution of the film/sensor, then it is considered as focus.
Consider the schema above. The green point is perfectly focused on the screen, meaning that its image is also a point on the film. The orange point, however, is further in the background and its image is a circle on the screen. If this circle is bigger than the resolution of the film, hence orange point is not focused, its image would be blurred. However, if the orange point is close enough to the green point, then its image is smaller than the resolution, and can be considered as focused.
The same analysis works for the yellow point which is closer to the lens than the green point.
The depth of field in photography is defined as the distance along the optical axis of a segment in which all point is focused.
Says, if the orange and the yellow point in the schematic above are on the limit of being focused, then their distance is the depth of field.
The relation between the depth of field and the aperture is described in this article.